ГРАНИЧНИЙ СТАН ДВУТАВРОВОГО АРМОВАНОГО ПЕРЕРІЗУ З ВИКОРИСТАННЯМ ПРУЖНОПЛАСТИЧНИХ ДІАГРАМ ДЕФОРМУВАННЯ МАТЕРІАЛІВ

Abstract

The paper considers a technique for constructing the strength area of a I-reinforced section. The concept of "section strength area" is used in structural calculations based on ultimate equilibrium. The strength area is a closed area in the coordinates "moment - longitudinal force". A specific feature of the section strength region is that inside the strength region the section operates in the elastic stage, and at its boundary it passes into the limiting state with the possibility of unlimited plastic deformation. The equations describing the boundary of the section strength region are often called yield conditions. The complexity of obtaining dependencies describing the boundary of the section strength region largely depends on what mathematical dependencies describe the physical properties of the materials from which the section is made. In this work, it is assumed that the material from which the section is made and the reinforcing material are deformed according to the law of an ideal elastoplastic body. Thus, the deformation diagrams of materials are described by the Prandtl diagram. Moreover, the material from which the section is made has different yield strengths in tension and compression. The reinforcing material has the same tensile and compressive yield strengths. When deriving the equations describing the strength region of the section, it was assumed that a bending moment and a longitudinal force applied in the center of the I-beam wall. Taking into account that the section of an I-beam can be asymmetrical and have asymmetric reinforcement, different equations are used to describe the upper and lower boundaries of the strength region. To construct the strength area, in the general case, it is necessary to solve the optimization problem - for a given value of the longitudinal force, find the extreme value of the moment, taking into account the constraints (equalities and inequalities). Analysis of the results obtained in this way for a symmetrically reinforced section made it possible to propose a simpler technique for constructing the strength area of a I-reinforced section without solving the optimization problem. Keywords: elastoplastic body, reinforced I-section, strength area, calculation by limit equilibrium